Multiconstrained Finite-Horizon Piecewise Deterministic Markov Decision Processes with Unbounded Transition Rates

Yonghui Huang () and Xianping Guo ()
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Yonghui Huang: School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
Xianping Guo: School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

Mathematics of Operations Research, 2020, vol. 45, issue 2, 641-659

Abstract: This paper studies a multiconstrained problem for piecewise deterministic Markov decision processes (PDMDPs) with unbounded cost and transition rates. The goal is to minimize one type of expected finite-horizon cost over history-dependent policies while keeping some other types of expected finite-horizon costs lower than some tolerable bounds. Using the Dynkin formula for the PDMDPs, we obtain an equivalent characterization of occupancy measures and express the expected finite-horizon costs in terms of occupancy measures. Under suitable assumptions, the existence of constrained-optimal policies is shown, the linear programming formulation and its dual program for the constrained problem are derived, and the strong duality between the two programs is established. An example is provided to demonstrate our results.

Keywords: piecewise deterministic Markov decision process; finite horizon; constrained problem; occupancy measure; linear program (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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